A thin infinite nonconducting sheet with uniform surface charge density s = 11.0

Question

A thin infinite nonconducting sheet with uniform surface charge density
s = 11.0·10^-6 C/m^2 lies in the y-z plane. A charge Q = 5.00 µC is located on the x axis at a distance x= 32.00 cm from the sheet as shown.
(a) Find the magnitude of the electric field at a point P with the coordinates x= y= 32.00 cm, z= 0.
[Answer: 7.609×105 N/C]

(b) What work must be done against the electric forces in order to move the charge Q from the position x= 32.00 cm to the position x= 18.00 cm on the x axis?
[Answer: 4.350×10-1 J]

Explanation / Answer

(a) Find the magnitude of the electric field at a point P with the coordinates x= y= 32.00 cm, z= 0. field due to the sheet is E1 = s/(20)   along x direction field due to Q is E2 = Q/(40y^2)       along y direction so the net field = (E1^2 + E2^2) = 7.606*10^5 N/C work = Q*E1*(x1 - x2) = Q*s/(20) *(x1 - x2) = 0.4348 J

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